This site contains several movies that illustrate the dynamics of spin. Dynamics is a boring subject without spin:
a translating body does nothing interesting, and an ideal particle behaves much as you would expect. Some of the
phenomena illustrated below are very complicated to understand, but very easy to observe. I hope these videos will help
to open a few eyes to the wonders of spin.
If you have trouble viewing the videos then go to
testpage or download RealPlayer.V.10

Note that the ball comes back from where it came
Note the spin of the ball and that it exits without spin in the direction that it entered.
Isn't it extraordinary that the ball returns almost exactly along its entry path? A light beam certainly wouldn't
do this, so strengthening the case for exercising caution when referring to the "particle theory of light". The particle
theory of light assumes that the particle has mass but no moment of inertia and that it has no physical size. I've never
seen a ball in the playground that fits this description!

Lambard's non-goal popped back to the keeper because of spin - to find out why, click here .

Downball - Simulation of a ball bouncing against a wall, hitting the wall first

(MPG) or
(CIN) or
(AVI) Note that the exit angle is not equal to the entry angle, and note the spin.
It is for this reason that I object to the "particle theory of light" being taught in schools without some kind
of clear indication that superballs (or any ball for that matter) do not behave as particles. How can kids be expected
to understand the particle theory of light if experiments that they can easily perform
with "particles" in the playground demonstrate that particles don't behave as
light does?

Downball - Simulation of a ball bouncing against a wall, hitting the floor first

(MPG) or
(CIN) or
(AVI) Note now that the exit angle is yet again different
from the entry angle. If the particle were to behave as if it were a beam of light then the exit path would be
parallel to the entry path. But then ball games in the playground wouldn't be nearly as much fun without spin!

Ball rolling up to a wall - normal incidence
First assume perfect friction conditions with the wall, allowing the rolling ball to grip momentarily onto the wall,
lifting itself up into the air.
(MPG) or
(CIN) or
(AVI) and a simulation
(MPG) or
(CIN) or
(AVI)

Note that the ball doesn't just bounce back - it jumps in the air
DRY WALL
The upward force that causes the ball to jump also causes the spin direction to reverse. This reversal of spin is exactly what
is needed for the ball ultimately to begin rolling back the other way.

Now if we assume that the wall is slippery, then the ball cannot be lifted up into the air. As a result there is no force from the wall
to change the direction of spin so the ball begins its return journey spinning the wrong way. Friction with the floor
gradually acts to reverse the spin direction, but
this friction force also slows the ball down and in the process the ball is almost brought to a complete halt.
(AVI)
... but now with a slippery wall the ball doesn't jump up
OILY WALL
This is completely counterintuitive - who'd have thought that lubricating the wall would cause the ball to bounce back more slowly?

Ball rolling up to a wall - incidence 45 degrees

(MPG) or
(CIN) or
(AVI)
- this is a top view.
Note that the ball does not reflect at 45 degrees. It is airborne and then it changes direction after the first bounce. Note also the change in spin as it bounces.

(AVI)
- ball on bat in a simple limit cycle
- note the ball hits the bat once per cycle
(JPG)

(AVI)
- ball on bat in a complex limit cycle
- the bat oscillates at twice the ball bounce rate and the ball height alternates
(JPG)

(AVI)
- ball on bat in chaotic motion
- this is the usual condition.
(JPG)

Modelling is difficult for three reasons:
1 - The impact is hard to model. Most people use "coefficient of restitution" and this is a simplistic approach.
But there are not many alternatives! I have used a coefficient of restitution e=0.9 for all the animations here. The biggest concern
is that impact is assumed to be instantaneous - which it isn't. A more-realsitic model has to include a spring at the contact
interface and this spring may itself be non-linear and dissipative.
2 - Even for a simple ball with a single contact point bouncing on a sinusoidally-moving table the problem is nonlinear and chaotic
solutions result. Solving such systems is not for the feint-hearted.
3 - Being a non-linear and chaotic system it is very sensitive to the method of modelling and also sensitive to initial conditions.
Then when it comes to modelling more realistic problems (for instance an object bouncing in the back of a truck on a bumpy road)
it is necessary to include multiple contacts and these add significant complexities and uncertainties.

The Matlab code used to generate this bat-on-ball motion can be found
here . This code comes with no guarantees.

The obvious question to ask is "how can the motion be modelled yet at the same time be unpredictable"? It is true that I have
made a mathematical model and I have simulated the motion to produce the animation here. But if an experiment were performed the
observed motion would not be the same as the prediction here. This is because the initial conditions used in the simulation cannot
be exactly the same as those in an experiment. Also the presence of small deviations from "ideal behaviour", for instance friction
or perhaps flexibility of the bearings, or lack of rigidity of the pendulum rod etc. etc. will lead to massive deviations from the
model predictions.

The Matlab code used to generate this chaotic doublependulum motion can be found
here . This code comes with no guarantees.

Toast always seems to land buttered-side down when you drop it.
This is because when it falls off the edge of a table it starts to rotate.
You can do good experiments with a small hard-back book (use a rubber band to hold the pages closed). The motion can be analysed using Newton's Laws of Motion, but it is
not as simple as analysts such as Matthews make out. Bacon et al. do it better.
There are three phases, "no slip", "slip" and "free fall". The first thing to do is to hold the book (or toast) over the edge of a table
so that it will just balance. Then push it just 1mm further and it will start to fall. At first the angular velocity of the book increases
gradually during the "no slip" phase until it reaches an angle of around 20o - 30o (depending on friction). At this point friction is insufficient
to prevent slip, but the book does not lose contact. During the "slip" phase (you can hear the book slip) the forces acting on the book are more-widely separated so the angular
acceleration is more rapid. This means that it is during this slipping phase that the book gains most of its angular velocity. Eventually the angular
motion causes the book to lose contact with the table and it then enters the "free fall" stage. The angular velocity is constant but simple projectile
motion requires that the book accelerate downwards at a rate of g = 9.81ms-1 and in the time it takes the book to turn through 180o it has fallen a distance of about 70cm.
This is the height of a typical table. What is remarkable is that this conclusion is not very sensitive to the exact starting position of the book (1mm, 2mm -
doesn't matter much) or the friction coefficient (anything between µ = 0.1 and 0.5 will give roughly the same answers. So it is no surprise that toast often lands
upside down.
For a fuller explanation see
here .
The Matlab code used to generate this falling toast motion can be found
here . This code comes with no guarantees.
Download a copy of the movie at (MPG) , (WMV) or
(AVI)

(MPG) or
(CIN) or
(AVI)
- Ball rolling on a sloping tableBecause this is a big video you may have trouble downloading it. It has to be big in order to
show the ball rolling on the sloping table before being spun up, then to show the spinup, then
showing the remarkable convection at 90 degrees to the expected direction.
Here is a smaller version:
(AVI)
Provided that you trust that the slope of the
table in the following two clips is the same, then these files are smaller and just as remarkable.
Ball on sloping table, table not spinning (AVI) or
(MPG)
or
(CIN)

(MPG) or
(CIN) or
(AVI)
- The same motion, but viewed from above
- note that it looks as if the ring makes a "flip", but this is an illusion resulting from the camera angle. The motion is in fact steady

The motion is governed by conservation laws (kinetic energy and moment of momentum). These laws are simple but solution
of the equations of motion (Euler's equations) is tricky, involving Jacobian Elliptic Functions. Matlab has been used to
procuce the following simulated motions:

Conservation of Moment of Momentum (Angular Momentum, if you prefer)
It is easy to write down the equations of motion in terms of energy and moment-of-momentum, but solution of the
equations is problematic. Here are two video simulations of the motion of the ball given two different initial
conditions.

Gabor Domokos and his
Gömböc -
as featured on the BBC "quiz" show QI, Fri 13 February 2009. You need to go about half way through (13m30s).
Best viewed in RealPlayer, but it has also been known to work in Windows Media Player.
(WMV)

This page contains low-resolution animated GIFs which should play automatically.
To view the video full-size then click on the
MPG ,
CIN or
AVI links,
choosing the one that plays best on your computer.
If you're having trouble viewing the full-size
videos then please go to
testpage .